Shock waves and characteristic discontinuities in ideal compressible two-fluid MHD

TL;DR

This paper analyzes ideal compressible two-fluid MHD, establishing conditions for the existence of shock waves, current-vortex sheets, and contact discontinuities, with results on their local-in-time existence under specific physical conditions.

Contribution

It introduces a symmetric form of two-fluid MHD equations and provides new criteria for the local-in-time existence of shock waves and discontinuities.

Findings

All compressive extreme shock waves exist locally in time with weak magnetic fields.

A sufficient condition for the existence of current-vortex sheets is derived.

Contact discontinuities exist locally if the Rayleigh-Taylor sign condition is met.

Abstract

We are concerned with a model of ideal compressible isentropic two-fluid magnetohydrodynamics (MHD). Introducing an entropy-like function, we reduce the equations of two-fluid MHD to a symmetric form which looks like the classical MHD system written in the nonconservative form in terms of the pressure, the velocity, the magnetic field and the entropy. This gives a number of instant results. In particular, we conclude that all compressive extreme shock waves exist locally in time in the limit of weak magnetic field. We write down a condition sufficient for the local-in-time existence of current-vortex sheets in two-fluid flows. For the 2D case and a particular equation of state, we make the conclusion that contact discontinuities in two-fluid MHD flows exist locally in time provided that the Rayleigh-Taylor sign condition on the jump of the normal derivative of the pressure is satisfied at the first moment.